In 1929, Neugebauer founded Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik (QS), a Springer series devoted to the history of the mathematical sciences, in which he published extended papers on Egyptian computational techniques in arithmetic and geometry, including the Moscow Papyrus, the most important text for geometry. Neugebauer had worked on the Moscow Papyrus in Leningrad in 1928.

In 1931, he founded the review journal Zentralblatt für Mathematik und ihre Grenzgebiete (Zbl), his most important contribution to modern mathematics. When Hitler became chancellor in 1933, Neugebauer was asked to sign an oath of loyalty to the new government, but he refused and was promptly suspended from employment. In 1934, he joined the University of Copenhagen as full professor of mathematics. In 1936, he published a paper on the method of dating and analyzing texts using diophantine equations. During 1935–37, he published a corpus of texts named Mathematische Keilschrift-Texte (MKT). MKT was a colossal work, in size, in detail, in depth, and its contents show that the riches of Babylonian mathematics far surpass anything one could imagine from a knowledge of Egyptian and Greek mathematics.

Neugebauer was also interested in chronology. He was able to reconstruct the Alexandrian Christian calendar and its origin from the Alexandrian Jewish calendar as of about the 4th century, at least 200 years prior to any other source for either calendar. Thus, the Jewish calendar was derived by combining the 19-year cycle using the Alexandrian year with the seven-day week, and was then slightly modified by the Christians to prevent Easter from ever coinciding with Passover. The ecclesiastical calendar, considered by church historians to be highly scientific and deeply complex, turned out to be quite simple. In 1988, by studying a scrap of Greek papyrus, Neugebauer discovered the most important single piece of evidence to date for the extensive transmission of Babylonian astronomy to the Greeks and for the continuing use of Babylonian methods for 400 years even after Ptolemy wrote the Almagest. His last paper, “From Assyriology to Renaissance Art,” published in 1989, detailed the history of a single astronomical parameter, the mean length of the synodic month, from cuneiform tablets, to the papyrus fragment just mentioned, to the Jewish calendar, to an early 15th-century book of hours.

In 1986 Neugebauer was awarded the Balzan Prize "for his fundamental research into the exact sciences in the ancient world, in particular, on ancient Mesopotamian, Egyptian and Greek astronomy, which has put our understanding of ancient science on a new footing and illuminated its transmission to the classical and medieval worlds. For his outstanding success in promoting interest and further research in the history of science" (Motivation of the Balzan General Prize Committee). Neugebauer donated the prize money of 250,000 Swiss francs to the Institute for Advanced Study.